Constrained optimization problem. perfect substitute utility function

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I have a midterm coming up so promptness in a response would be greatly appreciated. My question is if the utility function indicated perfect substitutes like the one in the video and prices are different, why would there not be a corner solution if we are solving for the consumer's optimal bundle? Py>Px so the consumer would buy all of x so that he/she is the best off give his/her exogenous income and prices. I might be missing something, but this should be a corner solution only with the consumer choosing a bundle with all of good x and none of good y. Correct me if I'm wrong. Thanks.

aarondowning